The three-day summit is the fifth between Mr Bush and Mr Putin, but their first meeting on Russian soil.

The two leaders met behind closed doors with only their national security advisers present, apparently taking some extra time to discuss some of the unresolved issues in their relations.

After formal talks, they signed the nuclear agreement, and a declaration on a new strategic partnership, in the ornate, gilded St Andrew's Hall of the Kremlin Palace.

Critics point out that many nuclear warheads will be placed in storage rather than destroyed as Russia had wanted.

And the BBC's Nick Bryant says that if this is a new strategic partnership as both sides claim, it is asymmetrical, weighted heavily in favour of America.

Distrust

Russia's sale of nuclear technology and conventional weapons to Iran also threaten to sour the new friendship.

In Berlin on Thursday, Mr Bush issued a stern warning about nuclear co-operation with what he considers a "rogue state".

The Moscow protests have been small scale

Russian Foreign Minister Igor Ivanov rejected the US fears, saying Moscow adhered to treaties on the non-proliferation of weapons.

But the BBC's Caroline Wyatt in Moscow says many Russians still view the US with distrust.

Ahead of Mr Bush's arrival, about 300 protesters demonstrated outside the US embassy in Moscow, although the protests were small compared to the tens of thousands who gathered in Berlin to show their anger at US policies.

Poultry and steel

As well as talks on arms, Mr Bush has been discussing economic ties between the USA and Russia.

Russia is hoping for US help to gain entry to the World Trade Organisation, but trade relations between the two have recently been marred by squabbles over poultry imports and US steel tariffs

Mr Bush said he was determined to get the US Congress to lift the 1974 Jackson-Vanik agreement, which restrict normal trade relations with Russia.

The US president is due to travel to Mr Putin's hometown of St Petersburg on Saturday .